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Simplifying 0.6x + 13 = x2 + -6 Reorder the terms: 13 + 0.6x = x2 + -6 Reorder the terms: 13 + 0.6x = -6 + x2 Solving 13 + 0.6x = -6 + x2 Solving for variable 'x'. Reorder the terms: 13 + 6 + 0.6x + -1x2 = -6 + x2 + 6 + -1x2 Combine like terms: 13 + 6 = 19 19 + 0.6x + -1x2 = -6 + x2 + 6 + -1x2 Reorder the terms: 19 + 0.6x + -1x2 = -6 + 6 + x2 + -1x2 Combine like terms: -6 + 6 = 0 19 + 0.6x + -1x2 = 0 + x2 + -1x2 19 + 0.6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19 + 0.6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + -0.6x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -0.6x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -0.6x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -0.6x + x2 = 0 + 19 -0.6x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -0.6x + x2 = 19 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 19 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 19 + 0.09 Combine like terms: 19 + 0.09 = 19.09 0.09 + -0.6x + x2 = 19.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 19.09 Calculate the square root of the right side: 4.369210455 Break this problem into two subproblems by setting (x + -0.3) equal to 4.369210455 and -4.369210455.Subproblem 1
x + -0.3 = 4.369210455 Simplifying x + -0.3 = 4.369210455 Reorder the terms: -0.3 + x = 4.369210455 Solving -0.3 + x = 4.369210455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 4.369210455 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 4.369210455 + 0.3 x = 4.369210455 + 0.3 Combine like terms: 4.369210455 + 0.3 = 4.669210455 x = 4.669210455 Simplifying x = 4.669210455Subproblem 2
x + -0.3 = -4.369210455 Simplifying x + -0.3 = -4.369210455 Reorder the terms: -0.3 + x = -4.369210455 Solving -0.3 + x = -4.369210455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -4.369210455 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -4.369210455 + 0.3 x = -4.369210455 + 0.3 Combine like terms: -4.369210455 + 0.3 = -4.069210455 x = -4.069210455 Simplifying x = -4.069210455Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.669210455, -4.069210455}
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